I'm not sure what you mean in your first question, but you could do the second one easily by just changing the point at which you define your zero value of gravitational potential energy to be. Remember that potential energies really only express themselves as forces and so it is the derivative of the potential which matters, I can add a constant on to any potential in order to make the numbers work out nicely for a particular problem since the derivative of that constant will be zero and hence it won't show up in a force.

No, the potential energy of a system may not always be only the gravitational energy and the elastic energy. The system may be under the influence of other forces like electric fields due to which it has other contributions to potential energy.